How to animate snow falling in cycles?
You definitely want to use a particle system for the falling snow flakes.

You could use a physics sim of some kind to create the "piling up" effect, but I don't think the result would be worth the sim calculation time. Also snow in real life piles up fairly slowly as far as what the eye can see, it doesn't look like a bucket of sand being poured on the ground.

If it were me I would create some sort of mesh object for the snow cover on the ground, and use shape keys to animate it slowly growing higher. The snow particles could just pass right through it or die on contact. This should work unless you need a super macro shot of the snow flakes.